RC circuits, consisting of a resistor (R) and a capacitor (C) in series or parallel configurations, are fundamental in understanding the principles of electronic filtering and timing applications. The response of an RC circuit to sudden voltage changes, such as switching on/off or shifting from high to low voltage, provides valuable insights into its operational behavior. This experiment focuses on the time constant (τ), a critical parameter that determines the circuit's response speed to these changes.

**Objective**

The aim is to observe and analyze the response of a simple RC circuit to a square wave input, highlighting the concept of the time constant (τ) and its impact on the circuit's transient behavior. Additionally, the experiment explores the effects of substituting a capacitor with an inductor, offering a comparative study of RC and RL circuits.

**Materials and Setup**

- Red Pitaya or similar device for signal generation and oscilloscope measurements
- Resistors (100 Ω), capacitors (10 nF), and optional inductors (1 mH) for circuit construction
- Alligator clips, wires (Ethernet cables recommended), and Y splitters for connection

**Experiment Procedure**

**RC Circuit Assembly:**Construct the RC circuit with the specified components. Connect the oscilloscope's input probe to the resistor's second lead and ground the capacitor using an alligator clip. Utilize a Y splitter for tidy connections and simple input/output management.**Signal Generation:**Set the Red Pitaya to output a square wave at a frequency ensuring observable transient effects, specifically chosen to be greater than 1/5τ.**Observation of Transient Response:**Measure the time it takes for the signal to reach 95% of its change, reflecting the circuit's time constant in action.**Substitution with an Inductor:**Replace the capacitor with an inductor to convert the setup into an RL circuit and observe the resulting changes.

**Analysis and Observations**

**RC Circuit Response:**The time constant (τ = R * C) fundamentally dictates how swiftly the RC circuit reacts to voltage changes. The experimental setup allows for direct observation of this behavior, showcasing the exponential charging and discharging of the capacitor. $τ = R \cdot C$**Inductor Substitution:**Swapping the capacitor for an inductor alters the circuit dynamics, introducing a different transient response characteristic of RL circuits. This comparison underlines the distinct ways in which capacitors and inductors store and release energy.

**Conclusion**

This experiment sheds light on the critical aspects of RC circuits, particularly their response to voltage changes as governed by the time constant (τ). Through practical observation and analysis, we gain a deeper understanding of filtering and timing mechanisms inherent in such configurations. The exploration extends to comparing RC and RL circuits, broadening our comprehension of transient responses in various circuit arrangements. The insights garnered from these experiments are instrumental in designing and analyzing circuits for a myriad of electronic applications, emphasizing the foundational role of RC and RL circuits in the field of electronics.